Modelling Health Care value is usually problematic as a result of are distributed in a non-normal method. Usually, there are a lot of $0 observations (i.e., people who don’t use any Health Care) and price distribution that’s strongly proper skewed amongst Health Care customers due a disproportionate variety of people with very excessive Health Care prices. This remark is well-known by Health economists however a complicating issue for modelers is mapping illness value to particular Health Care states. As an example, whereas the price of most cancers care could range primarily based on illness stage and whether or not the most cancers has progressed; the price of heart problems will differ if the affected person has a myocardial infarction.
A paper by Zhou et al. (2023) offers a pleasant tutorial on how one can estimate prices with illness mannequin states utilizing generalized linear fashions. The tutorial comprises for essential steps.
Step 1: Getting ready the dataset:
- The dataset usually requires calculating value for discrete time durations. As an example, if in case you have claims knowledge, you’ll have Information on value by date, however for analytic functions could wish to have a dataset with value Information by particular person (rows) with the columns being the fee by yr (or month). Alternatively, you could possibly create the unit of remark to be the person-year (or person-month) and every row can be a separate person-year document.
- Subsequent, one should specify the illness states. In every time interval, the particular person is assigned to a illness state. Challenges embrace figuring out how granular to make the states (e.g. simply MI vs timing since MI) and how one can deal with multi-state eventualities.
- When knowledge are censored one can (i) add a covariate to point knowledge are censored or (ii) exclude observations with partial knowledge. If value knowledge are lacking (however the affected person isn’t in any other case censored), a number of imputation strategies could also be used. Forming the time durations of study requires mapping to the choice mannequin’s cycle size, dealing with censoring appropriately, and doubtlessly reworking knowledge.
- A pattern knowledge set is proven under.
Step 2: Mannequin choice:
- The paper recommends utilizing a two-part mannequin with a generalized linear mannequin (GLM) framework, since OLS assumptions round normality and homoscedasticity within the residuals are sometimes violated.
- With the GLM, the anticipated worth of value is reworked non-linearly, as proven within the components under. You might be required to estimate each a hyperlink perform and the distribution of the error time period. “The preferred ones (mixtures of hyperlink perform and distribution) for healthcare prices are linear regression (identification hyperlink with Gaussian distribution) and Gamma regression with a pure logarithm hyperlink.)
- To mix the GLM with a two-part mannequin, one merely estimate the equation above on all constructive values after which calculates a logit or probit mannequin for the chance a person has constructive value.
Step 3: Choosing the ultimate mannequin.
- Mannequin choice first should think about which covariates are included within the regression which may be obtained by stepwise choice utilizing a pre-specified statistical significance. Nonetheless this can lead to over becoming. Various covariate choice methods embrace bootstrapping stepwise choice and penalized methods (e.g. least angle choice and shrinkage operator, LASSO). Interactions between covariates is also thought of.
- General match may be evaluated utilizing the imply error, imply absolute error and root imply squared error (the final is mostly used). Higher becoming fashions have smaller errors.
Step 4: Mannequin prediction
- Whereas predicted value are simple to do, the influence of illness state on value is extra advanced. The authors advocate the next:
For a one-part non-linear mannequin or a two-part mannequin, marginal results may be derived utilizing recycled prediction. IT contains the next two steps: (1) run two eventualities throughout the goal inhabitants by setting the illness state of curiosity to be (a) current (e.g. recurrent most cancers) or (b) absent (e.g. no most cancers recurrence); (2) calculate the distinction in imply prices between the 2 eventualities. Customary errors of the imply distinction may be estimated utilizing bootstrapping.
The authors additionally present an illustrative instance making use of this strategy to modeling hospital value related to cardiovascular occasions within the UK. The authors additionally present the pattern code in R as nicely and you’ll obtain that here.